数独_DFS剪枝，状态压缩，lowbit树

166. 数独

数独是一种传统益智游戏，你需要把一个 9×9 的数独补充完整，使得图中每行、每列、每个 3×3 的九宫格内数字 1∼9 均恰好出现一次。

请编写一个程序填写数独。

输入格式

输入包含多组测试用例。

每个测试用例占一行，包含 81 个字符，代表数独的 81 个格内数据（顺序总体由上到下，同行由左到右）。

每个字符都是一个数字（1−9）或一个 .（表示尚未填充）。

您可以假设输入中的每个谜题都只有一个解决方案。

文件结尾处为包含单词 end 的单行，表示输入结束。

输出格式

每个测试用例，输出一行数据，代表填充完全后的数独。

输入样例：

4.....8.5.3..........7......2.....6.....8.4......1.......6.3.7.5..2.....1.4......
......52..8.4......3...9...5.1...6..2..7........3.....6...1..........7.4.......3.
end

输出样例：

417369825632158947958724316825437169791586432346912758289643571573291684164875293
416837529982465371735129468571298643293746185864351297647913852359682714128574936

代码：

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

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<code-line class="line-numbers-rows"></code-line>    for(int i = 0; i < N; i++){ <code-line class="line-numbers-rows"></code-line>        row[i] = (1 << N) - 1; <code-line class="line-numbers-rows"></code-line>        col[i] = (1 << N) - 1; <code-line class="line-numbers-rows"></code-line>        cell[i / 3][i % 3] = (1 << N) - 1; <code-line class="line-numbers-rows"></code-line>    } <code-line class="line-numbers-rows"></code-line>    <code-line class="line-numbers-rows"></code-line>} <code-line class="line-numbers-rows"></code-line>void draw(int x, int y, int t, int is_set){ <code-line class="line-numbers-rows"></code-line>    int a = 1 << t; <code-line class="line-numbers-rows"></code-line>    <code-line class="line-numbers-rows"></code-line>    if(is_set){ <code-line class="line-numbers-rows"></code-line>        str[x * N + y] = t + '1'; <code-line class="line-numbers-rows"></code-line>        row[x] -= a; <code-line class="line-numbers-rows"></code-line>        col[y] -= a; <code-line class="line-numbers-rows"></code-line>        cell[x / 3][y / 3] -= a; <code-line class="line-numbers-rows"></code-line>    }else{ <code-line class="line-numbers-rows"></code-line>        str[x * N + y] = '.'; <code-line class="line-numbers-rows"></code-line>        row[x] += a; <code-line class="line-numbers-rows"></code-line>        col[y] += a; <code-line class="line-numbers-rows"></code-line>        cell[x / 3][y / 3] += a; <code-line class="line-numbers-rows"></code-line>    } <code-line class="line-numbers-rows"></code-line>} <code-line class="line-numbers-rows"></code-line>int get(int x, int y){ <code-line class="line-numbers-rows"></code-line>    return row[x] & col[y] & cell[x / 3][y / 3]; <code-line class="line-numbers-rows"></code-line>} <code-line class="line-numbers-rows"></code-line>int lowbit(int x){ <code-line class="line-numbers-rows"></code-line>    return x & -x; <code-line class="line-numbers-rows"></code-line>} <code-line class="line-numbers-rows"></code-line>void dfs(int cnt){ <code-line class="line-numbers-rows"></code-line>    if(!cnt){ <code-line class="line-numbers-rows"></code-line>        cout << str << endl; <code-line class="line-numbers-rows"></code-line>        flag = 1; <code-line class="line-numbers-rows"></code-line>        return ; <code-line class="line-numbers-rows"></code-line>    } <code-line class="line-numbers-rows"></code-line>    if(flag)return; <code-line class="line-numbers-rows"></code-line>    int MIN = 10; <code-line class="line-numbers-rows"></code-line>    int x, y; <code-line class="line-numbers-rows"></code-line>    for(int i = 0; i < N; i++){ <code-line class="line-numbers-rows"></code-line>        for(int j = 0; j < N; j++){ <code-line class="line-numbers-rows"></code-line>            if(str[i * N + j] == '.'){ <code-line class="line-numbers-rows"></code-line>                int state = get(i,j); <code-line class="line-numbers-rows"></code-line>                int sum = ones[state]; <code-line class="line-numbers-rows"></code-line>                <code-line class="line-numbers-rows"></code-line>                if(sum < MIN){ <code-line class="line-numbers-rows"></code-line>                    MIN = sum; <code-line class="line-numbers-rows"></code-line>                    x = i, y = j; <code-line class="line-numbers-rows"></code-line>                } <code-line class="line-numbers-rows"></code-line>            } <code-line class="line-numbers-rows"></code-line>            <code-line class="line-numbers-rows"></code-line>        } <code-line class="line-numbers-rows"></code-line>    } <code-line class="line-numbers-rows"></code-line>    //printf("x = %d  y = %d\n",x,y); <code-line class="line-numbers-rows"></code-line>    int state = get(x,y); <code-line class="line-numbers-rows"></code-line>    for(int i = state; i; i -= lowbit(i)){ <code-line class="line-numbers-rows"></code-line>        int t = m[lowbit(i)]; <code-line class="line-numbers-rows"></code-line>        draw(x,y,t,1); <code-line class="line-numbers-rows"></code-line>        dfs(cnt - 1); <code-line class="line-numbers-rows"></code-line>        draw(x,y,t,0); <code-line class="line-numbers-rows"></code-line>        <code-line class="line-numbers-rows"></code-line>    } <code-line class="line-numbers-rows"></code-line>} <code-line class="line-numbers-rows"></code-line>int main(){ <code-line class="line-numbers-rows"></code-line>    for(int i = 0; i < N; i++)  m[1 << i] = i; <code-line class="line-numbers-rows"></code-line>    for(int i = 0; i < M; i++) <code-line class="line-numbers-rows"></code-line>        for(int j = 0; j < N; j++) <code-line class="line-numbers-rows"></code-line>            ones[i] += (i >> j) & 1; <code-line class="line-numbers-rows"></code-line>    <code-line class="line-numbers-rows"></code-line>    <code-line class="line-numbers-rows"></code-line>    while(cin >> str, str[0] != 'e'){ <code-line class="line-numbers-rows"></code-line>        init(); <code-line class="line-numbers-rows"></code-line>        int cnt = 0; <code-line class="line-numbers-rows"></code-line>        for(int i = 0; i < N; i++){ <code-line class="line-numbers-rows"></code-line>            for(int j = 0; j < N; j++){ <code-line class="line-numbers-rows"></code-line>                char c = str[i * N + j]; <code-line class="line-numbers-rows"></code-line>                if(c != '.'){ <code-line class="line-numbers-rows"></code-line>                    draw(i,j,c - '1',1); <code-line class="line-numbers-rows"></code-line>                }else cnt++; <code-line class="line-numbers-rows"></code-line>            } <code-line class="line-numbers-rows"></code-line>            //cout << endl; <code-line class="line-numbers-rows"></code-line>        } <code-line class="line-numbers-rows"></code-line>        flag = 0; <code-line class="line-numbers-rows"></code-line>        dfs(cnt); <code-line class="line-numbers-rows"></code-line>    } <code-line class="line-numbers-rows"></code-line>    return 0; <code-line class="line-numbers-rows"></code-line>} </code-pre></div></div><div id="mCSB_3_scrollbar_vertical" class="mCSB_scrollTools mCSB_3_scrollbar mCS-minimal-dark mCSB_scrollTools_vertical" style="display: none;"><div class="mCSB_draggerContainer"><div id="mCSB_3_dragger_vertical" class="mCSB_dragger" style="position: absolute; min-height: 0px; height: 0px; top: 0px;"><div class="mCSB_dragger_bar" style="line-height: 0px;"></div></div><div class="mCSB_draggerRail"></div></div></div><div id="mCSB_3_scrollbar_horizontal" class="mCSB_scrollTools mCSB_3_scrollbar mCS-minimal-dark mCSB_scrollTools_horizontal" style="display: none;"><div class="mCSB_draggerContainer"><div id="mCSB_3_dragger_horizontal" class="mCSB_dragger" style="position: absolute; 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本文作者：从荣
本文链接：https://www.cnblogs.com/rongrongrong/p/15936405.html
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